I first learned this about molecules in fifth grade: a molecule is the smallest amount of a material that has the properties of that material. The textbook ended a discussion on oxygen telling us, "Oxygen atoms travel in pairs. Two oxygen atoms form an oxygen molecule. The oxygen molecule is the smallest amount that has the properties of oxygen."

Some time later -- I was still a child -- what may have been a college text wrote that an atom is the smallest amount with the properties of an element, while a molecule is the smallest amount of a compound with the properties of that compound. This addressed one confusion I had. Other concerns were about properties such as temperature, density, specific heat capacity, taste, odor -- properties that single molecules don't have. Later still, when I understood more of the subject, I realized that the fifth-grade textbook was right and the college text was wrong. Individual (free) oxygen atoms have rather different properties from oxygen molecules two atoms bound together. One major property difference is that at not-very-high temperatures, free oxygen atoms won't remain free oxygen atoms. They'll combine.

The ozone molecule is made of three oxygen atoms bound together. Ozone's properties are rather different from ordinary oxygen's. Ozone has an odor, for example. So, is ozone an element or a compound? I'll give my take on this question sometime later, in a comment.